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A217392
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Alternating sums of the squares of the ordered Bell numbers (number of preferential arrangements) A000670.
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4
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1, 0, 9, 160, 5465, 287216, 21643273, 2214984576, 295720862649, 49933547619472, 10404630591819497, 2622531836368780832, 786513638108085303193, 276793205620647080017968, 112961387008976003691598281, 52917386659933341334644891328, 28203267311410367019573922744697
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = sum((-1)^(n-k)*t(k)^2, k=0..n), where t = A000670 (ordered Bell numbers).
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MATHEMATICA
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t[n_] := Sum[StirlingS2[n, k]k!, {k, 0, n}]; Table[Sum[(-1)^(n-k)t[k]^2, {k, 0, n}], {n, 0, 100}]
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PROG
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(Maxima)
t(n):=sum(stirling2(n, k)*k!, k, 0, n);
makelist(sum((-1)^(n-k)*t(k)^2, k, 0, n), n, 0, 40);
(Magma)
A000670:=func<n | &+[StirlingSecond(n, i)*Factorial(i): i in [0..n]]>;
(PARI) for(n=0, 30, print1(sum(k=0, n, (-1)^(n-k)*(sum(j=0, k, j!*stirling(k, j, 2)))^2), ", ")) \\ G. C. Greubel, Feb 07 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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